Chapter 9 - Systems of Differential Equations - 9.2 Vector Formulation - True-False Review - Page 592: a

True

Given: $x'(t)=A(t)x(t)+b(t)$ To form a matrix multiplication $A(t)x(t)$, both $A(t)$ and $x(t)$ must have $n$n columns. Furthermore, $x'(t)$ is also a column $n$ vector function, hence $A(t)$ must have $n$ rows as well. The given mstatement is true.